How can I stream live data and present it in a line chart using PHP, cURL, ajax
I suggest you to use Google Charts's Line plot. See this jsFiddle example of how to add data automatically. This is simple as using the data.addRow([ DATA_INDEX, VALUE_1, VALUE_2, ... ]);
This use jQuery for plot initialization and "click" event. You'll have to make a loop in order to retrieve data and add it to the plot.
Any of the various JS chart libraries out there should be able to present a line chart for you via loading data up through ajax calls. Here are a few:
... and there are plenty more. Just find one that works best for you.
To run the ajax call that refreshes the charts every x-seconds, use something like this:
Call jQuery Ajax Request Each X Minutes
Also, take a look at this answer on the amCharts forum:http://www.amcharts.com/forum/viewtopic.php?id=12625